The course aims at students with an interest in optimization, combinatorics, geometry and algebra. The purpose of the course is to give an introduction to the theoretical background, to the computational techniques, and to applications of semidefinite optimization. In particular, after successful participation in the course students will be able to: explain the theory and algorithmic approach to solve semidefinite optimization problems, give examples of problems in optimization, combinatorics, geometry and algebra to which semidefinite optimization is applicable, solve semidefinite optimization problems with the help of Matlab-based solvers, recognize problems which can be tackled using semidefinite optimization.

Semidefinite optimization is a recent tool in mathematical optimization and can be seen as a vast generalization of linear programming. One can define it as minimizing a linear function of a symmetric, positive semidefinite matrix subject to linear constraints. Only twenty years ago it became clear that one van solve semidefinite optimization problems efficiently in theory and practice. Since then semidefinite optimization has become a frequently used tool of high mathematical elegance with big expressive and computational power.

The final grade will be based for 30% on homework assignments and for 70% on the final written exam. In addition weakly exercises will be posted at the course website, which will be discussed in class.